Index of dispersion – TheoremDex

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Index of dispersion

Formulation 0

Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number such that

(i)	\begin{equation} \mathbb{E} \|X\|^2 < \infty \end{equation}
(ii)	\begin{equation} \mathbb{E} X \neq 0 \end{equation}

The index of dispersion of $X$ is the D993: Real number \begin{equation} \text{Disp} X : = \frac{\text{Var} X}{\mathbb{E} X} \end{equation}

Also known as

Variance-to-mean ratio, Variance-to-expectation ratio, Dispersion-to-location ratio

Child definitions